Numerical simulations of shoaling internal solitary waves of elevation

Abstract

We present high-resolution, two-and three-dimensional direct numerical simulations of laboratory-scale, fully nonlinear internal solitary waves of elevation shoaling onto and over a small-amplitude shelf. The three-dimensional, mapped coordinate, spectral collocation method used for the simulations allows for accurate modelling of both the shoaling waves and the bottom boundary layer. We focus on wave-induced instabilities during the shoaling and de-shoaling processes. The shoaling of the waves is characterized by the formation of a quasi-trapped core which undergoes a spatially growing stratified shear instability at its edge and a lobe-cleft instability in its nose. Both of these instabilities develop and three-dimensionalize concurrently, leading to strong bottom shear stress. During the deshoaling process, the core breaks up and ejects fluid that forms a vortex-rich region near the down-sloping portion of the shelf. The flow in this region is highly turbulent and the bottom shear stress is extremely strong. Experiments with a corrugated bottom boundary are also performed. Boundary layer separation is found inside each of the corrugations during the wave's shoaling process. Our analyses suggest that all of these wave-induced instabilities can lead to enhanced turbulence in the water column and increased shear stress on the bottom boundary. Through the generation and evolution of these instabilities, the shoaling and de-shoaling cycles of internal solitary waves of elevation are likely to provide systematic mechanisms for material mixing and sediment resuspension. These mechanisms have significant environmental implications on the near-coastal regions of the world's oceans.iii

Vortex generation due to internal solitary wave propagation past a sidewall constriction

“…Simulations were performed with the Spectral Parallel Incompressible Navier–Stokes Solver (Subich, Lamb & Stastna 2013) which has been used extensively to model geophysical flows at laboratory scales (Olsthoorn & Stastna 2014; Xu, Subich & Stastna 2016; Deepwell et al. 2017; Harnanan et al.…”

“…Another possible definition of the wavelength is based on the horizontal extent of the along-channel velocity at the surface (Xu et al. 2016), although this is comparable to (2.7).

Figure 2.( a ) The background stratification.

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“…The constriction was uniform with depth. Simulations were performed with the Spectral Parallel Incompressible Navier-Stokes Solver (Subich, Lamb & Stastna 2013) which has been used extensively to model geophysical flows at laboratory scales (Olsthoorn & Stastna 2014;Xu, Subich & Stastna 2016;Deepwell et al 2017;Harnanan et al 2017). Temporal discretization was accomplished by a third-order multistep method with adaptive time step.…”

“…the distance from front flank to rear flank) is better approximated by 2L w . Another possible definition of the wavelength is based on the horizontal extent of the along-channel velocity at the surface (Xu et al 2016), although this is comparable to (2.7). Although the wavelength is partially constrained by the size of the domain, this constraint has minimal influence on the wave.…”

Asymmetries in gravity currents attributed to the nonlinear equation of state

“…The boundary conditions are free slip for velocity and no flux for temperature and the model achieves spectral accuracy. Previous studies have used SPINS to simulate the formation and propagation of gravity currents in numerous circumstances; Xu, Subich & Stastna (2016) and Xu & Stastna (2020) being two recent examples. The length of the domain is m and the height is m. The number of grid points in the horizontal and vertical directions are and respectively, and are uniformly spaced.…”